In the AP: 10, 5, 0, -5, ... the common difference d is equal to 5. Justify whether the above statement is true or false

Solution:

An arithmetic progression (AP) is a sequence where the two consecutive terms have the same common difference. It is obtained by adding the same fixed number to its previous term.

From the question, we have, AP: 10, 5, 0, -5, …..

The common difference can be found by,

a₂ - a₁ = 5 - 10 = - 5.

a₃ - a₂ = 0 - 5 = - 5.

a₄ - a₃ = -5 - 0 = - 5.

Here, d = -5

In the statement given, d = 5.

Therefore, the above statement is false.

✦ Try This: If the sum of the first n terms of an AP is 4n − n², what is the first term (that is S1)? What is the sum of the first two terms? What is the second term?

It is given that

Sum of first n terms

S_n = 4n - n²

First term will be n = 1

S₁ = 4(1) - 1² = 3

Sum of first two terms

S₂ = 4(2) - 2² = 8 - 4 = 4

So the second term is

a₂ = S2 - S1

Substituting the values

a₂ = 4 - 3 = 1

Therefore, the first term is 3, sum of first two terms is 4 and the second term is 1.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 5

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NCERT Exemplar Class 10 Maths Exercise 5.2 Sample Problem 1

In the AP: 10, 5, 0, -5, ... the common difference d is equal to 5. Justify whether the above statement is true or false

Summary:

In the AP: 10, 5, 0, -5, ... the common difference d is equal to 5. The above statement is false

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